This invention relates to the art of fracturing subterranean formations and more particularly to a method for determining fracture pressure closure and other parameters used in the process of designing and analyzing stimulation treatments of subterranean formations such as fracture treatments.
Hydraulic fracturing is a primary tool for improving well productivity by placing or extending channels from the wellbore to the reservoir. This operation is essentially performed by hydraulically injecting a fracturing fluid into a wellbore penetrating a subterranean formation and forcing the fracturing fluid against the formation strata by pressure. The formation strata or rock is forced to crack and fracture. Proppant is placed in the fracture to prevent the fracture from closing and thus, provide improved flow of the recoverable fluid, i.e., oil, gas or water.
A proper design of a fracturing treatment is a complex engineering discipline. The post-fracture production depends on multiple factors such as the reservoir permeability, porosity, pressure, injections rates and properties of the injected fluids. Among those factors, one of the most critical is the closure pressure, also called the minimum in-situ rock stress. The closure pressure is defined as the fluid pressure at which an existing fracture globally closes. The closure time is the time when the fluid in the fracture is completely leaked off into the formation and the fracture closes on its faces. The closure pressure forms the basis of all fracture analysis, and in particular of the pressure decline analysis. It is also used for proppant selection. Incorrect closure pressure could lead to incorrect interpretation of fluid efficiency and thus improper pad fluid volume, which could result in job failure or poorer hydrocarbon production.
Field procedures are routinely performed to estimate the closure pressure and other relevant parameters such as the in-situ fluid efficiency and leak-off coefficient. These procedures involve a calibration test or mini-frac. A mini-frac is an injection/shut-in/decline procedure. The designed viscosified fractured fluid (without proppant) is injected into the target formation at a constant rate for a period a time. Then, the well is shut in and a pressure decline analysis is performed. The mini-frac is essentially used for determining the fracture half-length, the fracture width, the fracture height, the fluid-loss coefficient, the formation""s Young""s modulus and the fluid efficiency. The fracture closure can also be identified from the decline curve as slope changes. However, other events such as fracture height recession and multiple permeable layers could lead to multiple points of slope change. In many cases, such as in naturally fractured formations with pressure dependent leak-off, the decline curve exhibits a gradual change of slope which makes picking the correct closure pressure difficult. For these reasons, different engineers often arrive at different closure pressures, leading to inconsistent or erroneous interpretations.
Separate closure tests have therefore been developed to specifically determine the closure pressure.
The most commonly used closure test technique is the step rate, generally performed with completion fluids or water. The thin fluid is injected into the target formation at increasing rates, ideally including both matrix rates and fracturing rates if possible. The matrix rates correspond to the flow into the formation before the fracture is opened, and fracturing rates are those that induce a pressure above the closure pressure so the fracture is opened and extended. A stabilized pressure is determined from the pressure record for each rate. The pressure is plotted against the flow rate. The ideal response will show data points falling approximately on two straight-line sections. The first straight line corresponds to the matrix flow at lower rates and has a steeper slope because a small rate increase will cause a relatively large pressure increase. The second straight line corresponds to the fracturing at higher rates and has flatter slope since once the fracture is opened, the fracturing pressure is much less sensitive to the flow rate. The intersection of the two lines is the fracture extension pressure, reflecting the minimal rate required to hydraulically extend a fracture. The extension pressure is an upper bound of closure pressure and often used as a direct approximation of closure pressure. Closure pressure can also be estimated from the intercept of the fracture extension line with the y-axis (corresponding to zero pump rate).
The step rate test can be affected by tubing friction and near-wellbore fracture xe2x80x9ctortuosityxe2x80x9d. The fracture tortuosity is the added pressure caused by various near-wellbore restrictions such as tortuous flow path through a micro annulus between cement and rock, limited number of perforations connecting with the fracture, multiple fracture branches, fracture reorientation as it propagates away from wellbore, etc. The tortuosity causes the measured pressure to be higher than the pressure inside the fracture and is rate dependent. As a result, the extension pressure determined from the step rate test includes a friction/tortuosity component. For high permeability reservoir, for which the extension rate is relatively high, the friction component is quite significant, making the extension pressure much greater than the closure pressure. Furthermore, both tubing friction and tortuosity are rate dependent and increase as rate increases. They may affect the pressure vs. rate plot in such a way that either the extension portion does not fit on a straight line or the slope is different from what should have been. The data points may therefore be dramatically altered, leading to interpretation errors.
Pump-in/flowback is another technique that has been used to determine closure pressure. After a period of injection, instead of shutting the well in, the fluid is flown back to surface-at a constant-rate. The pressure decline curve has a characteristic S-shape, changing from concaving upward (after the initiation of flow back, when the fracture is still open) to concaving downward (after fracture closure, when the pressure drops rapidly). The point of inflexion of the S-shaped curve yields an estimate of the closure pressure. When flowback ceases, the wellbore pressure recovers and reaches a plateau, which is called rebound pressure. The rebound pressure provides another approximation (usually a lower bound) of the closure pressure.
Though it looks attractive, the pump-in/flowback test is not widely used in the field. This is mainly due to the inconvenience of having to rig up a flowback line with an adjustable choke to keep the flowback rate constant. The adjustable choke has to be calibrated to determine the pressure reading corresponding to the flowback rate, and has to be manned during the flowback to maintain a constant rate.
Another technique that has been used to determine closure pressure is injection pulses during the pressure decline (i.e. shut-in period). A small volume of fluid is intermittently injected. At each injection, the wellbore pressure will exhibit a pressure pulse. The pulse will quickly dissipate and the pressure fall back to the normal decline curve if the fracture is still open. If the fracture is closed, the pulse will dissipate slower and the pressure will have a shift above the normal decline curve. Since the pulses are sparse, the pulses at best can bound the closure point between two consecutive pulses. The method cannot give an exact determination of the closure pressure. Furthermore, the pulses contaminated the normal decline behavior so that the determination of decline slope and leak-off properties may be compromised.
The present invention provides a new procedure for determining the fracture closure pressure of a full-scale fracture treatment of a subterranean formation.
The method of the present invention comprises injecting a fluid into the formation at a first generally constant rate Q to create a fracture having a volume, and dropping the pumping rate to significantly smaller feed rate q so that the volume of the fracture becomes constant, in other words, the injection and leak-off reach equilibrium. As the fracture volume becomes constant at equilibrium, the well is shut-in. The wellbore pressure is monitored and the closure pressure is determined from the analysis of the wellbore pressure using a time-function of the dimensionless xe2x80x9cshut-inxe2x80x9d time xcex94tD. According to preferred embodiment of the present invention, this function is based on the square-root of-the dimensionless xe2x80x9cshut-inxe2x80x9d time xcex94tD.
The small rate q should be less than the fluid leak-off rate in the fracture at the time of rate drop. The initial constant rate is preferably the expected fracturing rate of the full-scale treatment. According to a preferred embodiment, the rate ratio q/Q is preferably less than 0.2.
As a result of the injection rate decrease, the wellbore pressure initially declines as more fluid is leaked off into the formation than is injected in. The fluid leak-off decreases with time, and when the fracture approaches closure, the injection and leak-off reach equilibrium. As the fracture volume becomes constant at the equilibrium, the pressure levels off, which can be easily identified. From the measured pressure at the initial rate drop and at the equilibrium, the closure pressure can be estimated. The pressure drop at shut-in reflects the tortuosity and friction effects corresponding to the small injection rate. The estimated closure pressure can thus be corrected to account for tortuosity and friction. The method is operationally easy to implement in the field.
Additionally, with a modified time function that replaces the conventional G-function, the ideal decline curve becomes a straight line, and the slope is the same as the conventional G-plot. From the slope, the leak-off coefficient can be determined.